Worksheet on Rectangular – Polar Conversion

In math worksheet on rectangular – polar conversion; students can practice the questions on how to convert rectangular coordinates to polar coordinates and also convert polar coordinates to rectangular coordinates (vice-versa).

Recall the formula from polar to rectangular:

To convert polar coordinates to rectangular coordinates;

x = r cos θ, y = r sin θ

Recall the formula from rectangular to polar:

To convert rectangular coordinates to polar coordinates;

r = √(x² + y²) and tan θ = y/x or, θ = tan\(^{-1}\) y/x

To know more about the relation between the Cartesian co-ordinates and Polar co-ordinates and about more examples Click Here.

Follow the above formula to solve the below questions given in the worksheet on rectangular – polar conversion.

1. OX and OY are the cartesian axes of co-ordinates. Again 0 and OX are respectively the pole and initial line of a system of polar co-ordinates. With respect to these systems (i) if the polar co-ordinates of a point P be (2, 300), find the cartesian co-ordinates of the point; (ii) if the cartesian co-ordinates of a point P be (0, 2), find its polar co-ordinates.

2. Find the Cartesian co-ordinates of the points whose polar co-ordinates are :